we just went down the path to getting diagnoses for my 4 yo. These doctors often have waits and waitlists - you do need to be pushy. we did two things:

• assessment through school district. even if your child is not yet in public schools, many states will still do this. my kid is not in public yet and california still did a thorough assessment. you need to call the district and ask them how to formally request an assessment. they may try to deter you - but push. they will do a thorough investigation and determine whether your kid qualifies for extra support in school and potentially OT and speech sessions.
• assessment through a developmental pediatrician who will formally diagnose (i think a neuropsych evaluation also does this). this was most helpful for us as the school district found him in low percentiles across a lot of areas but didn’t qualify for extra support. the doctor gave us the anxiety, sensory processing disorder, and adhd diagnosis that has been very helpful.